Abstract
Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for [ x ( 0 ) = a 0 , x ˙ ( 0 ) = b 0 ] ) while the existing solution is determined for a particular case, especially for [ x ( 0 ) = a 0 , x ˙ ( 0 ) = 0 ] . The solution is easily transformed to perturbation solution. The method is used in various non-linear problems possessing second and more than second derivatives.
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